| Dewey Class |
516.35 |
| Title |
Generalizations of Thomae's Formula for Zn Curves ([Ebook]) / by Hershel M. Farkas, Shaul Zemel. |
| Author |
Farkas, Hershel M. |
| Added Personal Name |
Zemel, Shaul |
| Other name(s) |
SpringerLink (Online service) |
| Publication |
New York, NY : Springer , 2011. |
| Physical Details |
XVII, 354 pages : online resource. |
| Series |
Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt 1389-2177 ; ; 21 |
| ISBN |
9781441978479 |
| Summary Note |
This book provides a comprehensive overview of the theory of theta functions, as applied to compact Riemann surfaces, as well as the necessary background for understanding and proving the Thomae formulae. The exposition examines the properties of a particular class of compact Riemann surfaces, i.e., the Zn curves, and thereafter focuses on how to prove the Thomae formulae, which give a relation between the algebraic parameters of the Zn curve, and the theta constants associated with the Zn curve. Graduate students in mathematics will benefit from the classical material, connecting Riemann surfaces, algebraic curves, and theta functions, while young researchers, whose interests are related to complex analysis, algebraic geometry, and number theory, will find new rich areas to explore. Mathematical physicists and physicists with interests also in conformal field theory will surely appreciate the beauty of this subject.: |
| Contents note |
- Introduction.-Â 1. Riemann Surfaces -- 2. Zn Curves -- 3. Examples of Thomae Formulae -- 4. Thomae Formulae for Nonsingular Zn Curves -- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn Curves.-Appendix A. Constructions and Generalizations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.-Index. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
http://dx.doi.org/10.1007/978-1-4419-7847-9 |
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